Abstract:
Let ξj, j=0,1…, be independent identically distributed random variables with Eξj≠0 belonging to the domain of attraction of the normal law.
The main result is the following relation:
E{Nn∣Qn(x)≢0}∼1πlnn(n→∞)
where Qn(x)=∑nj=0ξjxj and Nn is the number of real roots of Qn.
Citation:
I. A. Ibragimov, N. B. Maslova, “On the expected number of real zeros of random polynomials. II. Coefficients with non-zero means”, Teor. Veroyatnost. i Primenen., 16:3 (1971), 495–503; Theory Probab. Appl., 16:3 (1971), 485–493
\Bibitem{IbrMas71}
\by I.~A.~Ibragimov, N.~B.~Maslova
\paper On the expected number of real zeros of random polynomials. II.~Coefficients with non-zero means
\jour Teor. Veroyatnost. i Primenen.
\yr 1971
\vol 16
\issue 3
\pages 495--503
\mathnet{http://mi.mathnet.ru/tvp2262}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=288824}
\zmath{https://zbmath.org/?q=an:0277.60052}
\transl
\jour Theory Probab. Appl.
\yr 1971
\vol 16
\issue 3
\pages 485--493
\crossref{https://doi.org/10.1137/1116052}
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